基于MATLAB分子物理學(xué)和熱學(xué)分析與設(shè)計(jì) 結(jié)業(yè)論文

1、基于MATLAB分子物理學(xué)和熱學(xué)分析與設(shè)計(jì) 摘 要：MATLAB是一種以矩陣運(yùn)算為基礎(chǔ)的交互式程序語言，是專門針對(duì)科學(xué)和工程中計(jì)算和繪圖的需求開發(fā)的。與其他計(jì)算機(jī)語言相比，具有簡(jiǎn)潔和智能化的特點(diǎn)，人機(jī)性能好。本文利用MATLAB的數(shù)值計(jì)算、可視化圖形處理和程序設(shè)計(jì)等特點(diǎn)，設(shè)計(jì)了一個(gè)有關(guān)于大學(xué)物理中分子物理學(xué)和熱學(xué)的應(yīng)用，旨在將復(fù)雜的麥克斯韋速度分布律的數(shù)值計(jì)算和繪圖簡(jiǎn)單化。關(guān)鍵詞：分子物理學(xué)；熱學(xué)；理想氣體；麥克斯韋速率分布律；分析設(shè)計(jì)；MATLAB引言在分子物理學(xué)和熱學(xué)中可知，由大量分子組成的氣體，因分子間的頻繁碰撞，各個(gè)分子的速度大小和方向瞬息萬變。任一時(shí)刻，某個(gè)分子具有多大的運(yùn)動(dòng)速率完全

2、是偶然的，可以是零到無窮大之間的任何值。1859年，英國(guó)物理學(xué)家麥克斯韋（J.C.Maxwell）從理論上導(dǎo)出了氣體分子速率分布律麥克斯韋速率分布律。利用MATLAB軟件靈活的數(shù)值計(jì)算與符號(hào)計(jì)算、簡(jiǎn)單的語句表達(dá)、簡(jiǎn)潔完善的圖形繪制、豐富的工具箱函數(shù)和簡(jiǎn)易的擴(kuò)展功能，將復(fù)雜的數(shù)學(xué)公式繪制成曲線，并研究單個(gè)參數(shù)的影響。1、 麥克斯韋速率分布律 *2.1 速率分布和分布函數(shù) 為了描述平衡態(tài)下氣體分子的速率分布，先將分子速率范圍分成許多相等的速率區(qū)間，然后通過試驗(yàn)或理論推導(dǎo)找出分布在各個(gè)速率區(qū)間內(nèi)的分子數(shù)與總分子數(shù)的比率。這些比率便給出了分子的速率分布。下表給出了時(shí)空氣分子的速率分布: 速率區(qū)間分子數(shù)

3、比率速率區(qū)間分子數(shù)比率700 7.7由表可知，300500的分子數(shù)占總數(shù)的比率最大。其余的分子數(shù)占總分子數(shù)的比率都比較小。為了精確地描述分子速率分布，應(yīng)將速率區(qū)間取得足夠小，使。這時(shí)可將表示為微分，以表示分布在的分子數(shù)，比率是速率的函數(shù)，而且可以認(rèn)為與成正比，因而可表示為速率分布函數(shù)物理意義：速率在v附近單位速率區(qū)間內(nèi)的分子數(shù)占總分子數(shù)的百分比，或者說為某一分子的速率在v附近單位速率區(qū)間內(nèi)的概率。分布在有限速率區(qū)間內(nèi)的分子數(shù)為=分布在整個(gè)速率區(qū)間的分子數(shù)顯然為分子總數(shù)，所以 歸一化條件 2.2 理想氣體分子的麥克斯韋速率分布律麥克斯韋速率分布律指出，在平衡狀態(tài)下，理想氣體分子速率分布在區(qū)間內(nèi)的

4、分子數(shù)占總分子數(shù)的百分比為T為氣體的熱力學(xué)溫度，u為氣體分子的質(zhì)量，k為玻爾茲曼常量。可得麥克斯韋速率分布函數(shù)為麥克斯韋速率分布曲線 （f(v)為縱軸，v為橫軸）2、 MATLAB仿真與分析先把麥克斯韋速率分布律列成一個(gè)子程序，以便經(jīng)常調(diào)用，并把一些常用的常數(shù)也放在其中，這樣主程序就簡(jiǎn)單了許多。在主程序中，定義變量的數(shù)值（如：T,mu和v等的數(shù)值大小或取值范圍），然后調(diào)用maxwell（T,mu,v）函數(shù)進(jìn)行數(shù)值計(jì)算，并利用plot（v,y）函數(shù)將計(jì)算結(jié)果繪制成圖形。如此三遍，便可以繪制出如上所示的三條不同條件下的麥克斯韋速率分布律曲線。由圖可以知道，速率分布曲線的形狀與氣體溫度T和分子質(zhì)量u

5、有關(guān)。溫度升高時(shí)，分子熱運(yùn)動(dòng)加劇，即速率較大的分子數(shù)占總分子數(shù)的百分率增大。另外，分布曲線還需滿足歸一化條件，所以溫度升高時(shí)，分布曲線向右移動(dòng)，的極大值減小，曲線變得較為平坦。M文件：function f=maxwell(T,mu,v)%mu-分子量，千克.摩爾1%v-分子速度%T-氣體的絕對(duì)溫度 R=8.31;%氣體常數(shù)k=1.381*10(-23);%玻爾茲曼常數(shù)NA=6.022*1023;%阿伏伽德羅常數(shù)m=mu/NA;%分子質(zhì)量f=4*pi*(m/(2*pi*k*T)(3/2).*exp(-m*v.2./(2*k*T).*v.*v;%麥克斯韋分布律*程序主體：clearT=200;mu

6、=28e-3;%給出T,mvv=eps:1500;%給出自變量數(shù)組y=maxwell(T,mu,v);%調(diào)用M函數(shù)文件plot(v,y),hold on%畫出分布曲線v1=400:600;%給定速度范圍y1=maxwell(T,mu,v1);%該范圍的分布fill(v1,600,400,y1,0,0,b)trapz(y1)%求該范圍概率積分T=300;mu=28e-3;y=maxwell(T,mu,v);plot(v,y)%改變T，畫曲線T=200;mu=2e-3;y=maxwell(T,mu,v);plot(v,y) %改變mu，畫曲線gtext(T=300,mu=28*10-3),%此語句

7、可以生成希gtext(T=200,mu=28*10-3), 臘字母及上標(biāo)（指gtext(T=200,mu=2*10-3), 數(shù)）hold offans =0.33263、 結(jié)論由上可以看出，MATLAB軟件在分子物理學(xué)和熱學(xué)方面有很大用處，它可以方便、快捷、清晰形象地解決分子物理學(xué)和熱學(xué)中的一些復(fù)雜問題，將數(shù)值計(jì)算和繪圖這類問題變成數(shù)字化，只需更改幾個(gè)數(shù)字就可以得到其他的結(jié)果。在實(shí)際應(yīng)用中，更多復(fù)雜的問題都可以用MATLAB來進(jìn)行方便快捷的解決，根據(jù)實(shí)際情況，靈活應(yīng)用MATLAB.參考文獻(xiàn)：1 劉勍，溫志賢.MATLAB基礎(chǔ)及應(yīng)用M南京：東南大學(xué)出版社，2011.2 王少杰，顧牡.新編基礎(chǔ)物理

8、學(xué)M北京：科學(xué)出版社，2009.3 孫凍梅.MATLAB在力學(xué)熱學(xué)教學(xué)中的應(yīng)用J教育教學(xué)論壇，2013年06期4 劉衛(wèi)國(guó).MATLAB程序設(shè)計(jì)與應(yīng)用（第二版）M北京：高等教育出版社，2006.5 張世功.MATLAB用于物理實(shí)驗(yàn)常見的數(shù)據(jù)處理J大學(xué)物理實(shí)驗(yàn),2007,20（4）8586.6 陳揚(yáng).MATLAB6.x圖形編程與圖像處理.西安：西安電子科技大學(xué)出版社，2002.7 吳利華.MATLAB在大學(xué)物理實(shí)驗(yàn)教學(xué)中的應(yīng)用J實(shí)驗(yàn)科學(xué)與技術(shù),2009,7(2):101- 103.8 蔡旭輝等.MATLAB 基礎(chǔ)與應(yīng)用教程M.北京:人民郵電出版社,20119 王沫然. MATLAB與科學(xué)計(jì)算M.北

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24、2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YW

25、RrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqvadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#

26、QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&M

27、uWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVku

28、m&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89A

29、mv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWp

30、azadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5ux

31、Y7JnD6YWRrWwcvR9CpbK!zn%MadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*adNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVk

32、um&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWw

33、cvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT

34、#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qY

35、pEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY

36、7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9Cpb

37、K!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazad

38、Nu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5p

39、Dx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NG

40、pP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89A

41、mYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89A

42、mYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%MzadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn

43、%Mz849GxGjqv$UE9wEwZ#QcadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE

44、%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6

45、X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!

46、zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U

47、E9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh

48、5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6

49、YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnG

50、K8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqvUE%&qYp

51、Eh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGp

52、P$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz

53、849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEw

54、Z#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2

55、zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9w